Abstract
Let be a von Neumann algebra without nonzero central abelian projections on a complex Hilbert space . Let pn(X1, X2, · · ·, Xn) be the polynomial defined by n indeterminates X1, · · ·, Xn and their Jordan multiple ∗-products. In this paper it is shown that a family 𝒟 = {dm}m∈ℕ of mappings such that , the identity map on satisfies the condition
for all U1, U2, · · ·, Un ∈ and for each m ∈ ℕ if and only if 𝒟 = {dm}m∈ℕ is an additive ∗-higher derivation.